Free vibration analysis of viscoelastic nano-sandwich beam with flexible core resting on orthotropic Pasternak medium using non local high order sandwich panel theory

In this paper, vibration analysis of nonlocal nano-sandwich beam is investigated considering the size effects and flexibility of the core. This nano-sandwich beam is made from double beam and a flexible core. In the analytical formulation, normal and shear stresses are considered for the core employing the high order sandwich panel theory. In this regard the high order sandwich panel theory is extended at nano-scale. The material properties of system are assumed viscoelastic using Kelvin–Voigt model. The elastic medium is simulated by orthotropic Pasternak medium. The final equations are governed by Hamilton’s principle. The Navier method is applied for obtaining the natural frequency response of nano sandwich beam. The effects of different parameters such as nonlocal parameter, structural damping, viscoelastic foundation, geometrical parameters and stiffness of the core are shown on the vibration behavior of nanostructure. The accuracy of the proposed method is verified by comparing its numerical predictions with other published works. The results show that with increasing the nonlocal parameter, the frequency decreases.